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It took a long time for politicians to accept that human actions were warming the planet. Climate scientists began warning that human actions in burning fossil fuels were changing the climate in the late 1980s.

The difficulty was how to put the scientific data into a simple form that the public and politicians could understand. Their first effort was to describe Earth as if it were covered by something that kept the heat in: the greenhouse effect.

That image is fairly benign but it was enough to spur the United Nations to hold an Earth Summit in Rio de Janeiro in 1992 on the potential impact for the Earth.

Every year since, the UN has held a conference to assess the world’s progress in dealing with climate change. From 1997 the conferences negotiated the Kyoto Protocol to establish legally binding obligations on developed countries to reduce their carbon emissions.

But few countries took these emissions reduction protocols seriously and almost none voluntarily took action.

Then, towards the end of last century, a group of scientists in Germany proposed a stunningly simple way to think about climate change. For the last 12,000 years, they said, Earth’s climate has fluctuated within a narrow band. So, to be on the safe side, we should prevent global average temperatures from rising more than 2°C above what they were at the dawn of industrialisation.

Hans Joachim Schellnhuber, a scientist on the advisory panel for then-German environment minister Angela Merkel : “We said that, at the very least, it would be better not to depart from the conditions under which our species developed. Otherwise we’d be pushing the whole climate system outside the range we’ve adapted to.”

Scientists soon compiled evidence that the risks increased alarmingly above the 2°C threshold: such as rapid sea-level rise, crop failures, the collapse of coral reefs and more destructive storms.

By the 2009 in Copenhagen, nearly every government in the world endorsed the 2°C limit. Countries responsible for more than 80% of global emissions agreed with the Copenhagen Accord, that “the increase in global temperature should be below 2°C, in a context of sustainable development, to combat climate change”.

Every year since then, the world’s leaders have met at UN climate conferences to squabble over policies. This year’s conference will take place in Paris in November, but, like its predecessors, it is unlikely to result in any action.

We have accepted the 2°C limit as a barrier, as if everything will be totally fine if we keep below 1.9°C of warming but we are doomed if we hit 2.1°C.

But climate scientists are now saying it is increasingly likely that we will soar past the 2°C limit and reach a terrifying 4°C by century’s end. The Earth’s average temperature has already risen 0.8°C since the 19th century. To get back on track for 2°C now would mean the sort of drastic emissions cuts usually associated with economic calamities, such as the collapse of the Soviet Union. And we’d have to repeat those cuts every year for decades.

In 2007 The UN’s Intergovernmental Panel on Climate Change (IPCC) published a that said the world could stay below 2°C, but only if we started cutting emissions immediately. Years passed and emissions kept rising.

Since the industrial era began about 370 gigatons of carbon (GtC) have been emitted into the atmosphere. Most of those emissions have come from burning coal.

Last year the IPCC published its that said we could still stay under 2°C if we cut emissions more drastically and kept total emissions under 1000GtC by 2100. But in that year alone more than 10 GtC were emitted.

Climate scientist and activist James Hansen said that and will have catastrophic consequences. He said total emissions must be kept under 500GtC by 2100 to bring carbon dioxide levels down to 350 parts per million (ppm) from the current level of 400 ppm, which is the highest they have been for 3 million years.

Part of the problem is that even with current levels of emissions, the inertia of the climate system means that not all of the warming that those emissions will cause has happened yet — a certain amount is “in the pipeline” and will only rear its head in the future.

The oceans absorb some of the heat, delaying atmospheric warming for decades or centuries. Hansen says taking this into account, 1000GtC would lead to a temperature rise of at least 3°C and the impacts from climate change would be after 2100.

We have delayed action for so long that the necessary emissions cuts will have to be extremely sharp.

The IPCC concluded in 2014 that if we want to stay below the 2°C limit, global emissions would have to decline by about 3.1% each year, on average, between 2010 and 2050, until they were about 72% below 2010 levels. Then emissions would have to keep falling until, by the end of the century, humans were hardly putting any greenhouse gases into the atmosphere.

To put that in perspective, global emissions declined for only a single year by just 1% after the 2008 financial crisis, during a brutal recession when factories and buildings around the world were closed. To stay below 2°C, we will have to triple that pace of cuts, and sustain it year after year.

In the year since the IPCC report was released, the world’s nations have continued to put off cutting emissions. The odds of staying below 2°C look increasingly unlikely.

Peter Frumhoff of the Union of Concerned Scientists said: “Ten years ago, it was possible to model a path to 2°C without all these heroic assumptions. But because we've dallied for so long, that's no longer true.”

If he and other scientists are right, what is the prospect for life at 3°C or 4°C?

It might not sound like much of a change, but the Earth was only 4°C to 7°C cooler during the last ice age when large parts of the Earth were covered by glaciers. The IPCC concluded that changing the world’s temperature in the opposite direction would bring similarly drastic changes.

In 2013, the World Bank on the projected effects of 4°C of warming. Global food production would plummet. In countries such as Bangladesh, Egypt, Vietnam and in large parts of Africa, rising seas would end agriculture. There would be extreme heatwaves, declining global food stocks and loss of ecosystems and biodiversity.

But the World Bank report said there was much it could not predict about the impact of 4°C warming. Would the impact be twice as bad as at 2°C? Or might the impacts combine exponentially?

Ominously, the World Bank report doubted whether humanity could adapt to a 4°C world. “Given that uncertainty remains about the full nature and scale of impacts,” the report said, “there is also no certainty that adaptation to a 4°C world is possible.”

So, should we concede that we have missed our chance to keep global warming to 2°C and accept a slightly higher target, such as 2.5°C or 3°C? This sounds easy enough; after all 3°C is not as bad as 4°C.

As Oliver Geden, a climate policy analyst at the German Institute for International and Security Affairs : “At some point scientists will have to declare that it’s game over for the 2°C target. But they haven’t yet because nobody knows what will happen if they call this thing off.”

The concern is that if the 2°C target, one of the few things on which everyone at global climate talks agrees, turns out to be impossible, those talks would become even less productive than they are now. The target itself would be open to negotiation and that would lead to endless unproductive discussion. It could allow the world to drift into a situation where 4°C or even 6°C becomes acceptable and even inevitable.

Another alternative is to abandon the negative target of a degree of warming, in favour of a positive, easier to measure goal such as increasing the proportion of carbon-free energy. For example the University of Colorado’s Roger Pielke has suggested we aim for a global increase from the current 13% to 90% renewable energy.

And maybe we should make fossil fuel companies pay the full social and environmental cost of their use.

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